Nonleptonic decays of \(B_{(s)}\)  mesons play an essential role in the flavour-physics programmes at current and future colliders. The prospects for ever more precise measurements are therefore excellent, and that precision must be matched by theoretical predictions if we aim for improving our understanding of the mechanism of quark flavour mixing and CP violation, or even for pursuing the quest for indirect signals of new physics. On the theoretical side the bottleneck for precision is the computation of the hadronic matrix elements, where QCD effects from many different scales arise. Several approaches have been developed
to get a handle on the hadronic matrix elements, each having its virtues and drawbacks. Factorisation frameworks such as PQCD [1]}, [2]} or QCD factorization (QCDF) [3]}, [4]}, [5]} factorise short- from long-distance physics in the heavy quark limit. However, in their present use, they don't allow for the computation of sub-leading power corrections in the heavy-quark expansion from first field-theoretical principles (see [6]} for a computation of annihilation amplitudes with light-cone sum rules). Flavour symmetries of the light quarks [7]}, [8]}, [9]} have the advantage of hardly requiring any assumption about the scales of the occurring QCD effects, and relate different decay channels to each other, thereby reducing the number of independent parameters. On the other hand, it is well-known that flavour \(SU(3)\) , \(U\) -spin and \(V\) -spin are severely broken by the strange-quark mass, and the lack of a rigorous implementation of flavour breaking can still be regarded as the main drawback of this approach. Dalitz plot analyses are mostly applied to three-body decays, and very important for phenomenology. They are mostly data-driven, but also QCD-based predictions have been worked out in recent years [10]}, [11]}, [12]}.
